---------------------------------------------------------------------------------
      name:  <unnamed>
       log:  /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/
> JEPSReplicationfiles/Main/mainreplication_v2.log
  log type:  text
 opened on:  27 May 2022, 13:29:17

. use "${main_data}/pol_v0.8.dta", clear
(Merges randomization data with pol_v0.5)

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Table 2&3: The impact of incentives, numeracy and congeniality on accuracy
. * Linear Probability model is used in these two tables
. * Table 2 for unincentivized paticipants
. * Table 3 for all participants
. *------------------------------------------------------------------------------
> -
. *------------------------------------------------------------------------------
> -
. * Table 2: The impact of numeracy and congeniality on accuracy (unincentivized)
. *------------------------------------------------------------------------------
> -
. * Adjust the label values to accomodate the table
. label var correct "Correct"

. label var incentive "Incentive"

. label var congenial "Congenial"

. label var numeracy "Numeracy"

. label var numsq "Numeracy$^2$"

. label var num_con "Numeracy $\times$ Congenial"

. label var in_num_con "Incentive $\times$ Numeracy $\times$ Congenial"

. label var in_con "Incentive $\times$ Congenial"

. label var in_num "Incentive $\times$ Numeracy"

. label var in_numsq "Incentive $\times$ Numeracy$^2$"

. label var in_numsq_con "Incentive $\times$ Numeracy$^2$ $\times$ Congenial"

. 
. * Equation 1 (without control variables) - Table 2 (1)
. reg correct  congenial numeracy numsq if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(3, 1012)        =       3.36
                                                Prob > F          =     0.0183
                                                R-squared         =     0.0097
                                                Root MSE          =     .49264

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0476817   .0154853     3.08   0.002     .0172947    .0780686
    numeracy |  -.0041211   .0096472    -0.43   0.669     -.023052    .0148097
       numsq |   .0032297   .0053494     0.60   0.546    -.0072676    .0137269
       _cons |    .413911   .0212437    19.48   0.000     .3722242    .4555977
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a1

. 
. * Equation 1 (with control variables) - Table 2 (2)
. reg correct  congenial numeracy numsq age i.gender i.race i.edu i.vote2016 if i
> ncentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(23, 992)        =       1.85
                                                Prob > F          =     0.0087
                                                R-squared         =     0.0370
                                                Root MSE          =     .49066

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0440777   .0156257     2.82   0.005     .0134144     .074741
      numeracy |  -.0052758   .0104198    -0.51   0.613    -.0257232    .0151716
         numsq |   .0045627   .0054242     0.84   0.400    -.0060815    .0152068
           age |   .0012948   .0010279     1.26   0.208    -.0007223     .003312
               |
        gender |
         Male  |   .0295244   .0332494     0.89   0.375    -.0357229    .0947716
        Other  |   .0958812   .3185844     0.30   0.764    -.5292955     .721058
      Not say  |   -.079291   .3601188    -0.22   0.826    -.7859731     .627391
               |
          race |
Non-hispani..  |   .0933386   .0768335     1.21   0.225    -.0574364    .2441135
     Hispanic  |   .1370002   .0456432     3.00   0.003     .0474319    .2265686
        Asian  |   .1469838   .0794183     1.85   0.065    -.0088633    .3028308
American In..  |   -.179895   .1572748    -1.14   0.253    -.4885245    .1287345
       Others  |   .0837699   .0991428     0.84   0.398    -.1107839    .2783236
Prefer not ..  |   .1880987   .1493701     1.26   0.208    -.1050189    .4812163
               |
           edu |
High school..  |  -.0522322   .0787397    -0.66   0.507    -.2067476    .1022833
 Some college  |  -.1249886   .0804256    -1.55   0.120    -.2828124    .0328352
 College grad  |  -.1238539   .0822144    -1.51   0.132    -.2851879    .0374801
    Post grad  |  -.0404907    .087334    -0.46   0.643    -.2118713    .1308899
        Other  |  -.2497285    .167701    -1.49   0.137    -.5788179    .0793609
               |
      vote2016 |
      Clinton  |  -.0412692   .0399892    -1.03   0.302    -.1197423    .0372039
Other candi..  |   .0713568   .0773191     0.92   0.356    -.0803708    .2230845
      No vote  |  -.0600709   .0460642    -1.30   0.193    -.1504655    .0303236
      Not say  |   .0700357   .0927954     0.75   0.451    -.1120621    .2521335
        Other  |  -.0069821   .1724326    -0.04   0.968    -.3453565    .3313924
               |
         _cons |   .4004989    .101748     3.94   0.000     .2008328     .600165
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a2

. 
. * Equation 2 (without control variables) - Table 2 (3)
. reg correct  congenial numeracy numsq num_con c.numsq#c.congenial  if incentive
> ==0, r

Linear regression                               Number of obs     =      1,016
                                                F(5, 1010)        =       2.68
                                                Prob > F          =     0.0206
                                                R-squared         =     0.0128
                                                Root MSE          =     .49236

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0562078   .0215525     2.61   0.009     .0139151    .0985006
    numeracy |  -.0047547   .0096216    -0.49   0.621    -.0236352    .0141258
       numsq |   .0035448   .0053345     0.66   0.507    -.0069232    .0140129
     num_con |   .0173542   .0097831     1.77   0.076    -.0018434    .0365517
             |
     c.numsq#|
 c.congenial |  -.0035158    .005488    -0.64   0.522     -.014285    .0072533
             |
       _cons |   .4136017   .0212399    19.47   0.000     .3719223     .455281
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a3

. 
. * Equation 2 (with control variables) - Table 2 (4)
. reg correct congenial numeracy numsq num_con c.numsq#c.congenial age i.gender i
> .race i.edu i.vote2016 if incentive==0, r

Linear regression                               Number of obs     =      1,016
                                                F(25, 990)        =       1.79
                                                Prob > F          =     0.0100
                                                R-squared         =     0.0391
                                                Root MSE          =     .49062

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |    .051305    .021638     2.37   0.018     .0088435    .0937666
      numeracy |  -.0058657   .0103928    -0.56   0.573    -.0262602    .0145289
         numsq |   .0048272   .0054083     0.89   0.372    -.0057858    .0154402
       num_con |   .0144968   .0098907     1.47   0.143    -.0049124     .033906
               |
       c.numsq#|
   c.congenial |  -.0029396   .0055384    -0.53   0.596    -.0138079    .0079287
               |
           age |   .0013101   .0010278     1.27   0.203    -.0007067     .003327
               |
        gender |
         Male  |   .0289133   .0332645     0.87   0.385    -.0363636    .0941903
        Other  |   .0839929   .3137002     0.27   0.789    -.5316007    .6995866
      Not say  |  -.0894089   .3541709    -0.25   0.801    -.7844209    .6056031
               |
          race |
Non-hispani..  |   .0857081   .0767263     1.12   0.264    -.0648567    .2362729
     Hispanic  |   .1346295   .0456742     2.95   0.003     .0450001    .2242589
        Asian  |   .1413512   .0797034     1.77   0.076    -.0150557    .2977581
American In..  |   -.193841   .1608378    -1.21   0.228    -.5094632    .1217811
       Others  |   .0804974   .0991661     0.81   0.417    -.1141025    .2750972
Prefer not ..  |   .1922432   .1484896     1.29   0.196    -.0991472    .4836337
               |
           edu |
High school..  |  -.0534703   .0782925    -0.68   0.495    -.2071086     .100168
 Some college  |  -.1245236   .0799888    -1.56   0.120    -.2814906    .0324434
 College grad  |   -.122037   .0817126    -1.49   0.136    -.2823867    .0383128
    Post grad  |    -.04209   .0868794    -0.48   0.628    -.2125789    .1283988
        Other  |  -.2528496   .1717622    -1.47   0.141    -.5899094    .0842102
               |
      vote2016 |
      Clinton  |  -.0432571   .0400854    -1.08   0.281    -.1219192    .0354051
Other candi..  |   .0656904   .0774404     0.85   0.396    -.0862759    .2176566
      No vote  |  -.0597979   .0459716    -1.30   0.194     -.150011    .0304151
      Not say  |   .0683138   .0932006     0.73   0.464    -.1145796    .2512072
        Other  |  -.0047392   .1748922    -0.03   0.978    -.3479412    .3384628
               |
         _cons |   .4018509   .1014929     3.96   0.000      .202685    .6010168
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a4

. 
. * Export Table 2 in Latex
. esttab  a1 a2 a3 a4 using "${main_main}/Table_2.tex" ,  ///
>                 nonumbers mtitles("(1)" "(2)" "(3)" "(4)") b(3) star(* 0.10 ** 
> 0.05  *** 0.01) se(3)  label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Main/Table_2.tex)

. eststo clear

. *------------------------------------------------------------------------------
> -
. * Table 3: The impact of incentives, numeracy, and congeniality on accuracy (al
> l participants)
. *------------------------------------------------------------------------------
> -
. * Equation 3 (without control variables) - Table 3 (5)
. reg correct incentive, r

Linear regression                               Number of obs     =      3,050
                                                F(1, 3048)        =       0.01
                                                Prob > F          =     0.9412
                                                R-squared         =     0.0000
                                                Root MSE          =     .49409

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   incentive |  -.0013994   .0189843    -0.07   0.941    -.0386228    .0358239
       _cons |   .4232283   .0155055    27.30   0.000     .3928261    .4536306
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a5

. 
. * Equation 3 (with control variables) - Table 3 (6)
. reg correct incentive age i.gender i.race i.edu i.vote2016, r

Linear regression                               Number of obs     =      3,050
                                                F(21, 3028)       =       1.38
                                                Prob > F          =     0.1160
                                                R-squared         =     0.0092
                                                Root MSE          =     .49344

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     incentive |  -.0018305   .0189514    -0.10   0.923    -.0389896    .0353285
           age |   .0003372   .0005951     0.57   0.571    -.0008296     .001504
               |
        gender |
         Male  |   .0396994   .0186028     2.13   0.033      .003224    .0761748
        Other  |  -.0710805   .1835674    -0.39   0.699    -.4310098    .2888489
      Not say  |   .2250088   .1773961     1.27   0.205    -.1228203    .5728378
               |
          race |
Non-hispani..  |    .033006   .0420589     0.78   0.433    -.0494609    .1154728
     Hispanic  |   .0547986   .0275072     1.99   0.046      .000864    .1087333
        Asian  |    .041658    .042932     0.97   0.332    -.0425207    .1258368
American In..  |  -.0310012   .1251877    -0.25   0.804    -.2764628    .2144604
       Others  |    .003936   .0594216     0.07   0.947    -.1125747    .1204468
Prefer not ..  |   .0453473   .0866308     0.52   0.601    -.1245138    .2152084
               |
           edu |
High school..  |  -.0017768   .0499827    -0.04   0.972    -.0997801    .0962266
 Some college  |  -.0421486    .051065    -0.83   0.409    -.1422743     .057977
 College grad  |  -.0463904    .051835    -0.89   0.371    -.1480259     .055245
    Post grad  |   .0293679   .0543959     0.54   0.589    -.0772887    .1360245
        Other  |  -.1762801   .1073709    -1.64   0.101    -.3868073     .034247
               |
      vote2016 |
      Clinton  |   .0087136   .0229911     0.38   0.705    -.0363661    .0537933
Other candi..  |   .0316978   .0437519     0.72   0.469    -.0540887    .1174843
      No vote  |  -.0321485   .0265273    -1.21   0.226     -.084162    .0198649
      Not say  |   .0245996   .0528824     0.47   0.642    -.0790895    .1282886
        Other  |   .1076193   .1187254     0.91   0.365    -.1251713    .3404099
               |
         _cons |   .3969256   .0626795     6.33   0.000      .274027    .5198243
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a6

. 
. * Equation 4 (without control variables) - Table 3 (7)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con, r

Linear regression                               Number of obs     =      3,050
                                                F(11, 3038)       =       3.03
                                                Prob > F          =     0.0005
                                                R-squared         =     0.0110
                                                Root MSE          =     .49217

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
   congenial |   .0562078   .0215311     2.61   0.009     .0139908    .0984249
    numeracy |  -.0047547    .009612    -0.49   0.621    -.0236015     .014092
     num_con |   .0173542   .0097734     1.78   0.076     -.001809    .0365174
       numsq |   .0035448   .0053293     0.67   0.506    -.0069045    .0139942
             |
     c.numsq#|
 c.congenial |  -.0035158   .0054825    -0.64   0.521    -.0142657     .007234
             |
   incentive |  -.0042888   .0259404    -0.17   0.869    -.0551514    .0465738
      in_con |  -.0420477   .0263432    -1.60   0.111    -.0937001    .0096046
      in_num |    .020978   .0118507     1.77   0.077    -.0022583    .0442142
    in_numsq |   .0008031   .0065144     0.12   0.902    -.0119699    .0135762
  in_num_con |  -.0019392   .0119926    -0.16   0.872    -.0254536    .0215751
in_numsq_con |   .0056917   .0066806     0.85   0.394    -.0074073    .0187908
       _cons |   .4136017   .0212189    19.49   0.000     .3719969    .4552064
------------------------------------------------------------------------------

. estadd local Controls "No"

added macro:
           e(Controls) : "No"

. est store a7

. 
. * Equation 4 (with control variables) - Table 3 (8)
. reg correct  congenial numeracy num_con numsq c.numsq#c.congenial incentive in_
> con in_num in_numsq in_num_con in_numsq_con age i.gender i.race i.edu i.vote201
> 6, r

Linear regression                               Number of obs     =      3,050
                                                F(31, 3018)       =       1.91
                                                Prob > F          =     0.0018
                                                R-squared         =     0.0189
                                                Root MSE          =     .49182

--------------------------------------------------------------------------------
               |               Robust
       correct | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
---------------+----------------------------------------------------------------
     congenial |   .0536165   .0213776     2.51   0.012     .0117003    .0955326
      numeracy |  -.0072531   .0098453    -0.74   0.461    -.0265572     .012051
       num_con |   .0155421   .0098004     1.59   0.113    -.0036741    .0347582
         numsq |   .0047381   .0053288     0.89   0.374    -.0057104    .0151865
               |
       c.numsq#|
   c.congenial |  -.0031997   .0054683    -0.59   0.558    -.0139217    .0075223
               |
     incentive |   .0005495   .0258811     0.02   0.983    -.0501969    .0512959
        in_con |   -.039508   .0262373    -1.51   0.132    -.0909529    .0119369
        in_num |   .0209554    .011893     1.76   0.078    -.0023637    .0442745
      in_numsq |  -.0009373   .0065254    -0.14   0.886     -.013732    .0118574
    in_num_con |   .0002677   .0120337     0.02   0.982    -.0233275    .0238629
  in_numsq_con |   .0052488   .0066847     0.79   0.432    -.0078583    .0183559
           age |   .0003351   .0005936     0.56   0.572    -.0008287    .0014989
               |
        gender |
         Male  |   .0337102   .0188173     1.79   0.073    -.0031858    .0706062
        Other  |  -.0724254   .1810909    -0.40   0.689    -.4274993    .2826486
      Not say  |   .2299411   .1786474     1.29   0.198    -.1203418    .5802239
               |
          race |
Non-hispani..  |   .0351098   .0427287     0.82   0.411    -.0486705    .1188901
     Hispanic  |   .0539071   .0274637     1.96   0.050     .0000576    .1077565
        Asian  |   .0384688   .0431129     0.89   0.372    -.0460649    .1230025
American In..  |  -.0453592   .1281377    -0.35   0.723    -.2966052    .2058868
       Others  |   .0043976   .0585208     0.08   0.940    -.1103471    .1191424
Prefer not ..  |   .0458225   .0866071     0.53   0.597    -.1239925    .2156374
               |
           edu |
High school..  |  -.0043455   .0500325    -0.09   0.931    -.1024467    .0937558
 Some college  |  -.0483161   .0511788    -0.94   0.345    -.1486649    .0520327
 College grad  |  -.0527306   .0521218    -1.01   0.312    -.1549284    .0494672
    Post grad  |   .0141819   .0547492     0.26   0.796    -.0931675    .1215314
        Other  |  -.1758306   .1066342    -1.65   0.099    -.3849136    .0332524
               |
      vote2016 |
      Clinton  |   .0027745   .0229367     0.12   0.904    -.0421986    .0477476
Other candi..  |   .0199474   .0439637     0.45   0.650    -.0662545    .1061494
      No vote  |  -.0366544   .0264879    -1.38   0.167    -.0885905    .0152817
      Not say  |   .0176233   .0530828     0.33   0.740    -.0864588    .1217053
        Other  |   .1206758    .117772     1.02   0.306    -.1102457    .3515973
               |
         _cons |   .3971535   .0644829     6.16   0.000     .2707186    .5235884
--------------------------------------------------------------------------------

. estadd local Controls "Yes"

added macro:
           e(Controls) : "Yes"

. est store a8

. 
. * Export Table 3 in Latex
. esttab  a5 a6 a7 a8 using "${main_main}/Table_3.tex" ,  ///
>                 nonumbers mtitles("(5)" "(6)" "(7)" "(8)" "(9)" "(10)") b(3) st
> ar(* 0.10 ** 0.05  *** 0.01) se(3)  label  ///
>                 replace         ///
>                 drop(age *gender* *race* *edu* *vote2016*) /// 
>                 scalars("Controls") ///
>                 tex addnotes("Note:Linear Probability Model with heterscedastic
> ity robust standard errors." "Control variables in the regression are age, gend
> er, race, education, and voting2016")                                     
(output written to /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis
> /Work/JEPSReplicationfiles/Main/Table_3.tex)

. eststo clear

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> -
. * Figure 2: Predicted probabilities of correctly interpreting the data
. *------------------------------------------------------------------------------
> -
. * For this figure, we generate the density distribution by using MC simulation 
> from logistic regresion to estimate equation 4
. * The program "Clarify" is necessary to run this simulation.
. * Please see "Clarify: Software for Interpreting and Presenting Statistical Res
> ults" (Tomz, Wittenberg, and King; 2001) for your reference.
. 
. * GRAPH1: TOP-LEFT Graph (Non-incentivized & Low numeracy)
. * Graph below is the no-incentives low numeracy graph that will be in the top-l
> eft of the four graphs
. * Low Numeracy, Incentive=0
. * For the three simulations below: num is set at 1 out of 6 questions correctly
>  solved, numeracy is set at -1.654, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 numsq_con -2.736 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |    .414777     .0331293     .3538985     .480009

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4500751     .0320072     .3868136    .5160451

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 0 num_con 0 numsq 2.736 numsq_con 0 incentive 0 
> in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4315789     .0207221      .390652    .4733457

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000     .414777    .0331293   .3113092   .5212264
          p2 |      1,000    .4500751    .0320072   .3592643   .5581642
          p3 |      1,000    .4315789    .0207221   .3628878    .498098

. *-------------------------------------------------------GRAPH1-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.33 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.54 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (17 0.50 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("Non-Incentivized", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("Low numeracy", size (medium))           
>                                                                                
>                                                   ///
>                                 name(topleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH2: TOP-RIGHT Graph (Non-incentivized & High numeracy)
. * Graph below is the no-incentives high numeracy graph that will be in the top-
> right of the four graphs
. * High Numeracy, Incentive=0
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=+1.654, incentive =0
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 numsq_con -2.736 in
> centive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3412753     .0305697     .2853986    .4041205

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4919936     .0322725     .4245296    .5522249

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 0 num_con 0 numsq 2.736 numsq_con 0 incentive 0 i
> n_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4132073     .0222973     .3701659    .4578785

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3412753    .0305697   .2176469   .4365709
          p2 |      1,000    .4919936    .0322725   .3969156    .577213
          p3 |      1,000    .4132073    .0222973    .351759   .5010664

. *-------------------------------------------------------GRAPH2-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(9 0.26 "Cong
> enial = -1", color (orange) size(small)))        ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(13.5 0.52 "Congenial = +1", color (green) size(small)))       /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (17 0.47 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 title("High numeracy", size (medium))          
>                                                                                
>                                                   ///
>                                 name(topright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH3: BOTTOM-LEFT Graph (Incentivized & Low numeracy)
. * Graph below is the incentives low numeracy graph that will be in the bottom-l
> eft of the four graphs
. * Low Numeracy, Incentive=1
. * For the three simulations below: num=1 out 6 questions correctly solved, nume
> racy=-1.654, incentive =1
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial -1 num_con 1.654 numsq 2.736 numsq_con -2.736 in
> centive 1 in_con -1 in_num -1.654 in_numsq 2.736 in_num_con 1.654 in_numsq_con 
> -2.736

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3995476     .0226184     .3538492    .4448489

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 1 in_con 1 in_num -1.654 in_numsq 2.736 in_num_con -1.654 in_numsq_con 2
> .736

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3896165     .0216532     .3479439    .4318439

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 0 num_con 0 numsq 2.736 numsq_con 0 incentive 1 
> in_con 0 in_num -1.654 in_numsq 2.736 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .3942013     .0158567     .3634901      .42549

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .3995476    .0226184   .3207869   .4715358
          p2 |      1,000    .3896165    .0216532   .3269216   .4563759
          p3 |      1,000    .3942013    .0158567   .3483119    .451009

. *-------------------------------------------------------GRAPH3-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(12 0.49 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(9 0.30 "Congenial = +1", color (green) size(small)))          /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (21 0.46 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("  Incentivized  ", orientation(vertical
> ) size(medium))                                                                
>                           ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botleft1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. * GRAPH4: BOTTOM-RIGHT Graph (Incentivized & High numeracy)
. * Graph below is the incentives high numeracy graph that will be in the bottom-
> right of the four graphs.*/
. * High Numeracy, Incentive=1*/
. * For the three simulations below: num=4.35 out 6 questions correctly solved, n
> umeracy=1.654, incentive =1*/
. 
. * Congenial = -1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial -1 num_con -1.654 numsq 2.736 numsq_con -2.736 in
> centive 1 in_con -1 in_num 1.654 in_numsq 2.736 in_num_con -1.654 in_numsq_con 
> -2.736

. simqi, prval(1) genpr(p1)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4016074     .0224075     .3583923    .4451614

Simqi generated the following new variable(s): p1

. drop b*

. 
. * Congenial = +1
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 1 in_con 1 in_num 1.654 in_numsq 2.736 in_num_con 1.654 in_numsq_con 2.736

. simqi, prval(1) genpr(p2)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |   .4936738     .0232105     .4509305    .5413223

Simqi generated the following new variable(s): p2

. drop b*

. 
. * Congenial = 0
. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 0 num_con 0 numsq 2.736 numsq_con 0 incentive 1 i
> n_con 0 in_num 1.654 in_numsq 2.736 in_num_con 0 in_numsq_con 0

. simqi, prval(1) genpr(p3)

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=1) |     .44774     .0160079     .4148356      .47884

Simqi generated the following new variable(s): p3

. drop b*

. 
. sum p1 p2 p3

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
          p1 |      1,000    .4016074    .0224075   .3137109   .4912746
          p2 |      1,000    .4936738    .0232105   .4127783   .5616685
          p3 |      1,000      .44774    .0160079   .3889008    .495255

. *-------------------------------------------------------GRAPH4-----------------
> ------------------------------------------------
. graph twoway    (kdensity p1, lcolor(orange) lwidth(medthick) text(10 0.32 "Con
> genial = -1", color (orange) size(small)))       ///
>                                 (kdensity p2, lcolor(green) lwidth(medthick) te
> xt(19 0.54 "Congenial = +1", color (green) size(small)))         /// 
>                                 (kdensity p3, lcolor(gs5) lwidth(medthick) text
> (23 0.51 "Congenial = 0", color (gs5) size(small)))                      ///
>                                 ,legend(off)                                   
>                                                                                
>                                                                           ///
>                                 ylabel("")                                     
>                                                                                
>                                                                                
>    ///
>                                 ytitle("")                                     
>                                                                                
>                                                                                
>    ///
>                                 xlabel(0.2 "20%" 0.3 "30%" 0.4 "40%" 0.5 "50%" 
> 0.6 "60%")                                                                     
>                                   ///
>                                 xtitle("Probability of correct interpretation o
> f data")                                                                       
>                                   ///
>                                 title("")                                      
>                                                                                
>                                                                                
>    ///
>                                 name(botright1, replace) scheme(plotplain)

. graph close

. drop p1 p2 p3

. *------------------------------------------------------------------------------
> ------------------------------------------------
. *----------------------------------------------------- GRAPH COMBINE-----------
> ------------------------------------------------
. graph combine topleft1 topright1 botleft1 botright1, scheme(plotplain)

. graph export "${main_main}/Figure_2.png", replace
file
    /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/JEPSRep
    > licationfiles/Main/Figure_2.png saved as PNG format

. graph close

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *------------------------------------------------------------------------------
> ----------------------------------------------------
. * Table 4: Differences in the predicted congeniality bias between less and more
>  numerate individuals at various levels of numeracy
. *------------------------------------------------------------------------------
> ----------------------------------------------------
. * For this table, we generate the probability density distribution of correct a
> nswers by using MC simulation from logistic regresion to estimate regression eq
> uation 4
. * We set the high/low numeracy at +/-1SD, +/-1.5SD and +/-2SD
. * We run the simulation similar to Figure 2. The difference in correct answers 
> between Low and High Numeracy is tested using ttest.
. * The standard deviation of the measure of numeracy is: 1SD = 1.654; 1.5SD = 2.
> 481; 2SD = 3.308
. * The formula used for standard deviation in t-test = S.E. * (sqrt(n)); where n
>  = 1,000; n is the number of montecarlo simulations performed to generate the d
> ata.
. *******************************************************************************
> *
. * Model SD 1
. *******************************************************************************
> *
. * Simulation 1
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -1.654
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654 numsq_con 2.73
> 6 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5504388     .0313196      .487387    .6129417
             Pr(correct=1) |   .4495612     .0313196     .3870582     .512613

First Difference: congenial 1  -1 num_con -1.654 1.654 numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0352647     .0454657    -.1276779    .0560213

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 2
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 1.654
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.73
> 6 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5081279     .0318749     .4406895    .5728944
             Pr(correct=1) |   .4918721     .0318749     .4271056    .5593105

First Difference: congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1517941     .0464921    -.2416572    -.056345

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 3
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -1.654
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -1.654 congenial 1 num_con -1.654 numsq 2.736 numsq_con 2.736 inc
> entive 1 in_con 1 in_num -1.654 in_numsq 2.736 in_num_con -1.654 in_numsq_con 2
> .736

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -1.654 1.654 numsq_con 2.73
> 6 -2.736 in_con 1 -1 in_num_con -1.654 1.654 in_numsq_con 2.736 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6108749     .0218631     .5670119    .6513774
             Pr(correct=1) |   .3891251     .0218631     .3486226    .4329881

First Difference: congenial 1  -1 num_con -1.654 1.654 numsq_con 2.736 -2.736 in_
> con 1 -1 in_num_con -1.654 1.654 in_numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0106017     .0317074     -.054122    .0725858

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 4
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 1.654
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 1.654 congenial 1 num_con 1.654 numsq 2.736 numsq_con 2.736 incen
> tive 1 in_con 1 in_num 1.654 in_numsq 2.736 in_num_con 1.654 in_numsq_con 2.736

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.73
> 6 -2.736 in_con 1 -1 in_num_con 1.654 -1.654 in_numsq_con 2.736 -2.736) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .505521     .0229586      .461436    .5496573
             Pr(correct=1) |    .494479     .0229586     .4503427     .538564

First Difference: congenial 1  -1 num_con 1.654 -1.654 numsq_con 2.736 -2.736 in_
> con 1 -1 in_num_con 1.654 -1.654 in_numsq_con 2.736 -2.736

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.0912489     .0314316    -.1503737   -.0238918

. drop b*

. *******************************************************************************
> *
. * Model SD 1.5
. *******************************************************************************
> *
. * Simulation 5
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy = -2.481 
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.481 congenial 1 num_con -2.481 numsq 6.155 numsq_con 6.155 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.481 2.481 numsq_con 6.15
> 5 -6.155) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5612433     .0507029      .468284    .6603519
             Pr(correct=1) |   .4387567     .0507029     .3396481     .531716

First Difference: congenial 1  -1 num_con -2.481 2.481 numsq_con 6.155 -6.155

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0196376      .078381    -.1351211    .1805915

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 6
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy = 2.481
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.481 congenial 1 num_con 2.481 numsq 6.155 numsq_con 6.155 incen
> tive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.481 -2.481 numsq_con 6.15
> 5 -6.155) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4982654     .0439444     .4117104     .586744
             Pr(correct=1) |   .5017346     .0439444      .413256    .5882896

First Difference: congenial 1  -1 num_con 2.481 -2.481 numsq_con 6.155 -6.155

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1566313     .0633359    -.2710657   -.0269146

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 7
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -2.481
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -2.481 congenial 1 num_con -2.481 numsq 6.155 numsq_con 6.155 inc
> entive 1 in_con 1 in_num -2.481 in_numsq 6.155 in_num_con -2.481 in_numsq_con 6
> .155

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -2.481 2.481 numsq_con 6.15
> 5 -6.155 in_con 1 -1 in_num_con -2.481 2.481 in_numsq_con 6.155 -6.155) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |    .614668     .0364938     .5395525    .6846997
             Pr(correct=1) |    .385332     .0364938     .3153003    .4604475

First Difference: congenial 1  -1 num_con -2.481 2.481 numsq_con 6.155 -6.155 in_
> con 1 -1 in_num_con -2.481 2.481 in_numsq_con 6.155 -6.155

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0201847     .0538368    -.0851595    .1236077

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 8
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy= 2.481
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 2.481 congenial 1 num_con 2.481 numsq 6.155 numsq_con 6.155 incen
> tive 1 in_con 1 in_num 2.481 in_numsq 6.155 in_num_con 2.481 in_numsq_con 6.155

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 2.481 -2.481 numsq_con 6.15
> 5 -6.155 in_con 1 -1 in_num_con 2.481 -2.481 in_numsq_con 6.155 -6.155) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4565263     .0309048     .3958308    .5184559
             Pr(correct=1) |   .5434737     .0309048      .481544    .6041692

First Difference: congenial 1  -1 num_con 2.481 -2.481 numsq_con 6.155 -6.155 in_
> con 1 -1 in_num_con 2.481 -2.481 in_numsq_con 6.155 -6.155

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1329161     .0422665    -.2138417   -.0480246

. drop b*

. *******************************************************************************
> *
. * Model SD 2
. *******************************************************************************
> *
. * Simulation 9
. * No incentive and Low numeracy
. * Incentive = 0 and Numeracy= -3.308
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.308 congenial 1 num_con -3.308 numsq 10.943 numsq_con 10.943 i
> ncentive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.308 3.308 numsq_con 10.9
> 43 -10.943) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .5712199     .0827549      .411236    .7380886
             Pr(correct=1) |   .4287801     .0827549     .2619114     .588764

First Difference: congenial 1  -1 num_con -3.308 3.308 numsq_con 10.943 -10.943

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0832507     .1310801    -.1664702    .3362243

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 10
. * No incentive and High numeracy
. * Incentive = 0 and Numeracy= 3.308
. * Congenial = -1 for conservative and Congenial = +1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=-1) - Pr(correct=1|congenial=+1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.308 congenial 1 num_con 3.308 numsq 10.943 numsq_con 10.943 inc
> entive 0 in_con 0 in_num 0 in_numsq 0 in_num_con 0 in_numsq_con 0

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.308 -3.308 numsq_con 10.9
> 43 -10.943) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4888693      .070304     .3498591    .6225991
             Pr(correct=1) |   .5111307      .070304     .3774009    .6501409

First Difference: congenial 1  -1 num_con 3.308 -3.308 numsq_con 10.943 -10.943

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1506497     .1021858    -.3387377     .057845

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 11
. * Incentive and Low numeracy
. * Incentive = 1 and Numeracy= -3.308 
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy -3.308 congenial 1 num_con -3.308 numsq 10.943 numsq_con 10.943 i
> ncentive 1 in_con 1 in_num -3.308 in_numsq 10.943 in_num_con -3.308 in_numsq_co
> n 10.943

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con -3.308 3.308 numsq_con 10.9
> 43 -10.943 in_con 1 -1 in_num_con -3.308 3.308 in_numsq_con 10.943 -10.943) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .6092862     .0610567     .4817383    .7279153
             Pr(correct=1) |   .3907138     .0610567     .2720847    .5182617

First Difference: congenial 1  -1 num_con -3.308 3.308 numsq_con 10.943 -10.943 i
> n_con 1 -1 in_num_con -3.308 3.308 in_numsq_con 10.943 -10.943

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |   .0237335     .0907347    -.1508695    .1976465

. drop b*

. *------------------------------------------------------------------------------
> -
. * Simulation 12
. * Incentive and High numeracy
. * Incentive = 1 and Numeracy = 3.308
. * Congenial = +1 for conservative and Congenial = -1 for liberal
. * We find the predicted differences in probability that partisans will correctl
> y interpret the data
. * Prob difference = Pr(correct=1|congenial=1) - Pr(correct=1|congenial=-1)
. set seed 2121985

. estsimp logit correct numeracy congenial num_con numsq numsq_con incentive in_c
> on in_num in_numsq in_num_con in_numsq_con, r

Iteration 0:   log pseudolikelihood = -2077.1171
Iteration 1:   log pseudolikelihood = -2060.3642
Iteration 2:   log pseudolikelihood = -2060.3582
Iteration 3:   log pseudolikelihood = -2060.3582

Logistic regression                               Number of obs   =       3050
                                                  Wald chi2(11)   =      31.72
                                                  Prob > chi2     =     0.0008
Log pseudolikelihood = -2060.3582                 Pseudo R2       =     0.0081

------------------------------------------------------------------------------
             |               Robust
     correct | Coefficient  std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
    numeracy |  -.0213004    .039569    -0.54   0.590    -.0988542    .0562534
   congenial |   .2338905   .0911154     2.57   0.010     .0553076    .4124734
     num_con |   .0725903     .04073     1.78   0.075    -.0072391    .1524197
       numsq |   .0146061   .0220022     0.66   0.507    -.0285174    .0577296
   numsq_con |  -.0145652   .0231445    -0.63   0.529    -.0599275    .0307971
   incentive |  -.0138831   .1076481    -0.13   0.897    -.2248694    .1971032
      in_con |  -.1758884   .1107432    -1.59   0.112     -.392941    .0411642
      in_num |   .0873478   .0488918     1.79   0.074    -.0084783     .183174
    in_numsq |   .0029486   .0269216     0.11   0.913    -.0498168    .0557139
  in_num_con |  -.0094642   .0500093    -0.19   0.850    -.1074806    .0885522
in_numsq_con |   .0233749   .0281577     0.83   0.406    -.0318131     .078563
       _cons |   -.353564   .0882796    -4.01   0.000    -.5265888   -.1805391
------------------------------------------------------------------------------

Simulating main parameters.  Please wait....
% of simulations completed: 8% 16% 25% 33% 41% 50% 58% 66% 75% 83% 91% 100% 

Number of simulations  : 1000
Names of new variables : b1 b2 b3 b4 b5 b6 b7 b8 b9 b10 b11 b12

. setx numeracy 3.308 congenial 1 num_con 3.308 numsq 10.943 numsq_con 10.943 inc
> entive 1 in_con 1 in_num 3.308 in_numsq 10.943 in_num_con 3.308 in_numsq_con 10
> .943

. simqi, fd(prval(1)) changex(congenial 1  -1 num_con 3.308 -3.308 numsq_con 10.9
> 43 -10.943 in_con 1 -1 in_num_con 3.308 -3.308 in_numsq_con 10.943 -10.943) pr

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
             Pr(correct=0) |   .4003458     .0482304     .3074632    .5025674
             Pr(correct=1) |   .5996542     .0482304     .4974326    .6925368

First Difference: congenial 1  -1 num_con 3.308 -3.308 numsq_con 10.943 -10.943 i
> n_con 1 -1 in_num_con 3.308 -3.308 in_numsq_con 10.943 -10.943

      Quantity of Interest |     Mean       Std. Err.    [95% Conf. Interval]
---------------------------+--------------------------------------------------
          dPr(correct = 1) |  -.1788522      .068628    -.3161612   -.0473496

. drop b*

. *------------------------------------------------------------------------------
> -
. *The difference in the probabilty of correct answers between Low and High Numer
> acy individuals is tested using a ttest. 
. *The formula used for standard deviation in t-test = S.E. * (sqrt(n)); where n 
> = 1,000; 
. *n is the number of montecarlo simulations in each of the Simulations 1 through
>  12.
. *------------------------------------------------------------------------------
> -
. 
. * Simulation1/2 SD = 1 No-incentive - Low vs High Numeracy
. ttesti 1000 -.0352647 1.437752  1000 -.1517941 1.470209 

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000   -.0352647    .0454657    1.437752   -.1244839    .0539545
       y |   1,000   -.1517941    .0464921    1.470209   -.2430275   -.0605607
---------+--------------------------------------------------------------------
Combined |   2,000   -.0935294     .032532    1.454875   -.1573296   -.0297292
---------+--------------------------------------------------------------------
    diff |            .1165294     .065028               -.0110005    .2440593
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.7920
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9634         Pr(|T| > |t|) = 0.0733          Pr(T > t) = 0.0366

. 
. * Simulation3/4 SD = 1 Incentive - Low vs High Numeracy
. ttesti 1000 .0106017 1.002676  1000 -.0912489  0.9939545 

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0106017    .0317074    1.002676    -.051619    .0728224
       y |   1,000   -.0912489    .0314316    .9939545   -.1529284   -.0295694
---------+--------------------------------------------------------------------
Combined |   2,000   -.0403236    .0223467     .999374   -.0841488    .0035016
---------+--------------------------------------------------------------------
    diff |            .1018506    .0446464                .0142921    .1894091
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.2813
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9887         Pr(|T| > |t|) = 0.0226          Pr(T > t) = 0.0113

. 
. * Simulation5/6 SD = 1.5 No-incentive - Low vs High Numeracy
. ttesti 1000 .0196376 2.478625  1000 -.1566313 2.002857

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0196376     .078381    2.478625   -.1341727    .1734479
       y |   1,000   -.1566313    .0633359    2.002857    -.280918   -.0323446
---------+--------------------------------------------------------------------
Combined |   2,000   -.0684969     .050412    2.254493   -.1673624    .0303687
---------+--------------------------------------------------------------------
    diff |            .1762689    .1007721               -.0213605    .3738983
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.7492
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9598         Pr(|T| > |t|) = 0.0804          Pr(T > t) = 0.0402

. 
. * Simulation7/8 SD = 1.5 Incentive - Low vs High Numeracy
. ttesti 1000 .0201847 1.702469  1000 -.1329161 1.336584

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0201847    .0538368    1.702469   -.0854615    .1258309
       y |   1,000   -.1329161    .0422665    1.336584   -.2158574   -.0499748
---------+--------------------------------------------------------------------
Combined |   2,000   -.0563657    .0342573    1.532031   -.1235494     .010818
---------+--------------------------------------------------------------------
    diff |            .1531008     .068446                .0188678    .2873338
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   2.2368
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9873         Pr(|T| > |t|) = 0.0254          Pr(T > t) = 0.0127

. 
. * Simulation9/10 SD = 2 No-incentive - Low vs High Numeracy
. ttesti 1000 .0832507 4.145117  1000 -.1506497 3.231399

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0832507    .1310801    4.145117   -.1739732    .3404746
       y |   1,000   -.1506497    .1021858    3.231399   -.3511731    .0498737
---------+--------------------------------------------------------------------
Combined |   2,000   -.0336995    .0831226    3.717357   -.1967156    .1293166
---------+--------------------------------------------------------------------
    diff |            .2339004    .1662045               -.0920519    .5598527
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.4073
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9203         Pr(|T| > |t|) = 0.1595          Pr(T > t) = 0.0797

. 
. * Simulation11/12 SD = 2 Incentive - Low vs High Numeracy
. ttesti 1000 .0237335 2.869283  1000 -.1788522 2.170208

Two-sample t test with equal variances
------------------------------------------------------------------------------
         |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
       x |   1,000    .0237335    .0907347    2.869283    -.154319     .201786
       y |   1,000   -.1788522     .068628    2.170208   -.3135238   -.0441806
---------+--------------------------------------------------------------------
Combined |   2,000   -.0775593    .0569136    2.545255   -.1891756    .0340569
---------+--------------------------------------------------------------------
    diff |            .2025857    .1137655               -.0205257    .4256971
------------------------------------------------------------------------------
    diff = mean(x) - mean(y)                                      t =   1.7807
H0: diff = 0                                     Degrees of freedom =     1998

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.9624         Pr(|T| > |t|) = 0.0751          Pr(T > t) = 0.0376

. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. *******************************************************************************
> ****************************************************************
. drop _est*

. log close
      name:  <unnamed>
       log:  /Users/pavitra/Dropbox/Data/DataCleaning/DataCleaning_Analysis/Work/
> JEPSReplicationfiles/Main/mainreplication_v2.log
  log type:  text
 closed on:  27 May 2022, 13:29:33
---------------------------------------------------------------------------------
